## Circular law for the sum of random permutation matrices

Publication
, Journal Article

Basak, A; Cook, N; Zeitouni, O

Published in: Electronic Journal of Probability

January 1, 2018

Let Pn1, …, Pnd be n × n permutation matrices drawn independently and uniformly at random, and set Snd := ∑ℓ-1d Pnℓ. We show that if log12n/(log log n)4 ≤ d = O(n), then the empirical spectral distribution of Snd/√d converges weakly to the circular law in probability as n → ∞.

### Duke Scholars

## Published In

Electronic Journal of Probability

## DOI

## EISSN

1083-6489

## Publication Date

January 1, 2018

## Volume

23

## Related Subject Headings

- Statistics & Probability
- 4905 Statistics
- 0105 Mathematical Physics
- 0104 Statistics

### Citation

APA

Chicago

ICMJE

MLA

NLM

Basak, A., Cook, N., & Zeitouni, O. (2018). Circular law for the sum of random permutation matrices.

*Electronic Journal of Probability*,*23*. https://doi.org/10.1214/18-EJP162Basak, A., N. Cook, and O. Zeitouni. “Circular law for the sum of random permutation matrices.”

*Electronic Journal of Probability*23 (January 1, 2018). https://doi.org/10.1214/18-EJP162.Basak A, Cook N, Zeitouni O. Circular law for the sum of random permutation matrices. Electronic Journal of Probability. 2018 Jan 1;23.

Basak, A., et al. “Circular law for the sum of random permutation matrices.”

*Electronic Journal of Probability*, vol. 23, Jan. 2018.*Scopus*, doi:10.1214/18-EJP162.Basak A, Cook N, Zeitouni O. Circular law for the sum of random permutation matrices. Electronic Journal of Probability. 2018 Jan 1;23.

## Published In

Electronic Journal of Probability

## DOI

## EISSN

1083-6489

## Publication Date

January 1, 2018

## Volume

23

## Related Subject Headings

- Statistics & Probability
- 4905 Statistics
- 0105 Mathematical Physics
- 0104 Statistics